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Topic: Introduction to Arithmetic

	SMILE PROGRAM MATHEMATICS INDEX
		Arithmetic, Graphs and Visuals, Algebra and Trigonometry, and Miscellaneous.
		An Introduction to Pi and the Area of a Circle by Edwina R. Justice - Gunsaulus Scholastic Academy
		An Introduction to Estimation and Measurements by Christeen Brown - Robert Fulton Elementary
	www.iit.edu /~smile/mathinde.html (2771 words)

	Arithmetic - Wikipedia, the free encyclopedia
		Arithmetic or arithmetics (from the Greek word αριθμός = number) is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple daily counting to advanced science and business calculations.
		The prehistory of arithmetic is limited by a very small number of small artifacts indicating a clear conception of addition and subtraction, the best-known being the Ishango Bone from Africa, dating from 18,000 BCE.
		Since the introduction of the electronic calculator, which can perform the algorithms far more efficiently than humans, an influential school of educators has argued that mechanical mastery of the standard arithmetic algorithms is no longer necessary.
	en.wikipedia.org /wiki/Arithmetic (1385 words)

	Arithmetic Coding Tutorial
		If needed, a more basic implementation of arithmetic coding is described in references #2 and #4 (see reference section at bottom of page).
		In the Korfhage method of arithmetic coding, the intervals between 0 and 1 are continually broken down for each additional character.
		For a further example, below is a table illustrating the arithmetic coding for all possible strings of the given alphabet A, B, and C (see exercises 13 and 14 in Korfhage, Chapter 2).
	www.sis.pitt.edu /~jfondy/IS_2140/Arithmetic.htm (953 words)

	Dynamic of arithmetic: Introduction
		Children have acquired a host of impressive skills by the time they are taught formal arithmetic: they have learned a language and can use vision for autonomous navigation in a hostile environment.
		Arithmetic, it seems, is not an easy skill to come by.
		Two elementary arithmetic skills are considered: adult memory for multiplication facts and children's errors in long (multicolumn) multiplication.
	www.dallaway.com /acad/dphil/intro.html (1582 words)

	Basic arithmetic coding by Arturo Campos
		Arithmetic coding, is entropy coder widely used, the only problem is it's speed, but compression tends to be better than Huffman can achieve.
		The idea behind arithmetic coding is to have a probability line, 0-1, and assign to every symbol a range in this line based on its probability, the higher the probability, the higher range which assigns to it.
		The algorithm of arithmetic coding makes that if ever the msb of both high and low match are equal, then they'll never change, this is how can output the higher bits of the output infinite number, and continue working with just 16 bits.
	www.arturocampos.com /ac_arithmetic.html (1638 words)

	Untitled
		The output from an arithmetic coding process is a single number less than 1 and greater than or equal to 0.
		This is obviously a contrived example, but it does illustrate the point that arithmetic coding is able to compress data at rates much better than 1 bit per byte when the symbol probabilities are right.
		The code for the encoder as well as the decoder were first published in an article entitled "Arithmetic Coding for Data Compression" in the February 1987 issue of "Communications of the ACM", by Ian H. Witten, Radford Neal, and John Cleary, and is being published here with the author's permission.
	www.dogma.net /markn/articles/arith/part1.htm (5152 words)

	Decimal arithmetic - Introduction and rationale
		The arithmetic was designed as a full-function decimal extended floating point arithmetic, directly implementing the rules that people are taught at school.
		The precision of the arithmetic is freely selectable by the user, not limited to a choice from one or two alternatives; where necessary, calculations may be made using thousands of digits.
		The arithmetic was developed over several years, based directly on user feedback and requirements, and in consultation with professional mathematicians and data processing experts.
	www2.hursley.ibm.com /jsr13/decintro.html (1426 words)

	Using affine arithmetic for reachability computation (Site not responding. Last check: 2007-10-27)
		It seems the interval arithmetic is one of the most promising ways of performing the computation in higher-order state space.
		The introduction of affine arithmetic [1] is another way to avoid the error explosion.
		In the application of affine arithmetic, there is the problem of introducing too many noise variables whereas only a few are dominant.
	www.andrew.cmu.edu /user/zhih/aa/test_affine.html (1044 words)

	Modular Arithmetic — An Introduction
		As shown by the preceding examples, one of the powers of modular arithmetic is the ability to show, often very simply, that certain equations and systems of equations have no integer solutions.
		Without modular arithmetic, we would have to find all of the solutions and then see if any turned out to be integers.
		Of course, we don't need the formality of modular arithmetic in order to compute this, but when we do this kind of computation in our heads, this is really what we are doing.
	www.math.rutgers.edu /~erowland/modulararithmetic.html (1827 words)

	Interactivate: Lessons
		Introduces students to modular (clock) arithmetic and how modular arithmetic can be used to encode messages using simple shift, multiple and affine ciphers.
		Can be tailored for practice of all types of single operation arithmetic ranging from simple addition to operations with integers and decimals.
		Introduction and fine points of using bar graphs and histograms.
	www.shodor.org /interactivate/lessons (1154 words)

	DataCompression.info - Arithmetic Coding (Site not responding. Last check: 2007-10-27)
		Arithmetic coding is a method of encoding data using a variable number of bits.
		An arithmetic encoder doesn't have to use an integral number of bits to encode a symbol.
		In this particular case, A and B are a compressor and decompressor that use arithmetic coding.
	datacompression.info /ArithmeticCoding.shtml (2613 words)

	An Introduction to Arithmetic Coding
		Arithmetic coding is a data compression technique that encodes data (the data string) by creating a code string which represents a fractional value on the number line between 0 and 1.
		Arithmetic coding differs considerably from the more familiar compression coding techniques, such as prefix (Huffman) codes.
		This paper presents the key notions of arithmetic compression coding by means of simple examples.
	domino.research.ibm.com /tchjr/journalindex.nsf/0/aa3c6bd1731fbf0485256bfa0067f5bb (188 words)

	Introduction to Modular Arithmetic (Site not responding. Last check: 2007-10-27)
		Modular Arithmetic is a form of arithmetic dealing with the remainders after integers are divided by a fixed "modulus" m.
		Basically, it is a kind of integer arithmetic that reduces all numbers to ones that belongs to a fixed set [0...
		In this case, our fixed modulus is 6, so we say "mod 6." Here, operations of addition and multiplication with integers will result in a number that is divisible by 6 with a remainder of either 0, 1, 2, 3, 4, or 5.
	jwilson.coe.uga.edu /EMAT6680/Parsons/MVP6690/Essay1/modular.html (423 words)

	Nicomachus biography
		Nicomachus wrote Arithmetike eisagoge (Introduction to Arithmetic) which was the first work to treat arithmetic as a separate topic from geometry.
		However Introduction to Arithmetic does contain quite elementary errors which show that Nicomachus chose not to give proofs of his results because he did not in general have such proofs.
		Arab translations of Nicomachus's Introduction to Arithmetic were important and in [Centaurus 30 (3) (1987), 212-239.',5)" onmouseover="window.status='Click to see reference';return true">5] Brentjes studies the influence of these Arabic translations.
	www-groups.dcs.st-and.ac.uk /~history/Biographies/Nicomachus.html (1223 words)

	Arithmetic lattices in SU(n,1) (Site not responding. Last check: 2007-10-27)
		The purpose of this note is to provide an accessible introduction to arithmetic lattices in SU(n,1).
		The mathematical goal is two-fold; give the classification of arithmetic lattices in SU(n,1) and prove that there are infinitely many commensurability classes of lattices of first and second type.
		For the construction of infinitely many commensurability classes for each type, some background is needed; for instance, at the least the Hasse norm theorem and the Hasse invariant for a simple algebra over a number field.
	www.ma.utexas.edu /~dmcreyn/ComplexArithmeticI.html (112 words)

	Nicomachus of Gerasa (fl.c. 100 A.D.) : Library of Congress Citations (Site not responding. Last check: 2007-10-27)
		1926 Title: Introduction to arithmetic, translated into English by Martin Luther D'Ooge; with studies in Greek arithmetic, by Frank Egleston Robbins and Louis Charles Karpinski.
		Heading: Nicomachus, of Gerasa References: nna Nicomachus Gerasenus Nichomachus, of Gerasa Nicomaque, de Gberase Nikomachos, von Gerasa Nicomachus, the Pythagorean Notes: LCCN 26-9423: His Introduction to arithmetic, 1926 -- (hdg.: Nicomachus Gerasenus; usage: Nicomachus of Gerasa) LC data base, 10-26-84 -- (hdg.: Nicomachus Gerasenus; usage: Nichomachus of Gerasa) Enc.
		Introduction to arithmetic Notes: The thirteen books of Euclid's Elements, 1955, c1952: -- t.p.
	www.mala.bc.ca /~mcneil/cit/citlcnico.htm (570 words)

	Introduction to MPFI
		The basic principle of interval arithmetic consists in enclosing every number by an interval containing it and being representable by machine numbers: for instance it can be stored as its lower and upper endpoints and these bounds are machine numbers, or as a centre and a radius which are machine numbers.
		The arithmetic operations are extended for interval operands in such a way that the exact result of the operation belongs to the computed interval.
		The purpose of an arbitrary precision interval arithmetic is on the one hand to get guaranteed results, thanks to interval computation, and on the other hand to obtain accurate results, thanks to multiple precision arithmetic.
	pauillac.inria.fr /cdrom/www/mpfi/eng.htm (724 words)

	Ray's Arithmetic
		Ray's Arithmetics students learn arithmetic, increase their reading comprehension skills, and learn to think rather than plod through page after page of addition or subtraction problems with a one line direction at the top of each page.
		Teachers every-where, throughout the length and breadth of the land, are familiar with it's pages, and millions of pupils have gained their arithmetic knowledge from the study of it's principles.
		I hope this forum will be of assistance to those using Ray's Arithmetic and that it will be helpful to those who are considering it for use in their children's education.
	www.raysarithmetic.com /view/raysarithmetic/raysarithmetic.htm (7619 words)

	Amir Said Pages - FastAC - FastHF
		The code can be used as a companion to my Introduction to Arithmetic Coding [1,2], enabling students to understand how arithmetic coding works, and some of its implementation problems and solutions.
		While this may seem a contradiction with the first objective (truly efficient vs. simple), it happens that the new AC implementations can actually be both, thanks to the fact that they basically use arithmetic, which is supported with great efficiency and low cost in most current processor (including those for embedded systems, DSP, etc.) [1,2,3].
		It is basically the code used for the experiments in ref. [3], in which we compare the speed of different types of implementations, and stress the need to consider the encoder/decoder information throughput as a measure of efficiency and speed.
	www.cipr.rpi.edu /~said/FastAC.html (411 words)

	Arithmetic - Introduction
		In this chapter we will explore the integer arithmetic capabilities of the C programming language.
		The answer is that it might matter if an arithmetic overflow occurred during the calculation, the problems of arithmetic overflow will be discussed, briefly, later in this chapter.
		The value of an assignment expression may, of course, be assigned to a variable.
	www.scit.wlv.ac.uk /cbook/cchap3.html (4032 words)

	The Arithmetic of Nichomachus of Gerasa by Jay Kappraff for the Nexus Network Journal vol.2 no.4 October 2000
		Notice that the arithmetic and harmonic means insure the repetition of the ratios 2:3 and 3:4 to which they correspond.
		For example, place the generalized arithmetic and harmonic means between 12 and 36 in Table 6 and the common arithmetic and harmonic means between 18 and 54 in Table 7.
		Just as for Table 5 based on the ratio 1:2, each element of the Red sequence is the arithmetic mean of the pair of elements of the Blue series that brace it, while each element of the Blue series is the harmonic mean of the pair of elements from the Red series that brace it.
	www.nexusjournal.com /Kappraff.html (3392 words)

	Decimal Arithmetic - Introduction (Site not responding. Last check: 2007-10-27)
		A correct implementation of this specification is a decimal arithmetic which conforms to the requirements of the IEEE standard 854-1987,
		As of July 2003 only minor changes are expected; the principles of unnormalized values and arithmetic have been agreed by the 754 committee.
		Appendix A describes a simplified subset of the full arithmetic which implements the decimal floating-point arithmetic defined in the ANSI standard X3.274-1996
	www2.hursley.ibm.com /decimal/daintro.html (343 words)

	The MPFR Library
		SCSLib, a fast and lightweight multiple-precision library supporting the four arithmetic operations, developed in the Arenaire project at ENS-Lyon (France); the precision (210 bits by default) is fixed at compile time.
		The PreciseFloating (floating-point arithmetic library) project in Java, by Daniel Aioanei: directed rounding, rational arithmetic and arbitrary precision arithmetic based on regular continued fraction expansions.
		This calculator implements a rational arithmetic, with a fallback to some kind of multiple-precision fixed-point arithmetic (integer multiplied by a configurable epsilon).
	www.mpfr.org (717 words)

	Modular Arithmetic Index (Site not responding. Last check: 2007-10-27)
		On these pages you can learn about modular arithmetic, which is arithmetic on a circle instead of a number line.
		A calculator for arithmetic (+, -, x) on a clock.
		Some mathematical ideas from modular arithmetic used in RSA Fairly readable; high school/cA> Fairly readable; high school/college level.
	www.math.csusb.edu /faculty/susan/modular/modular.html (295 words)

	[13] I need source for arithmetic coding (Site not responding. Last check: 2007-10-27)
		Look also in ftp://munnari.mu.oz.au/pub/arith_coder C language source code for adaptive arithmetic coding based on the Witten-Neal-Cleary source code is in http://www.cipr.rpi.edu/wheeler/ac/ This version uses structures for the coder, decoder and data model instead of global variables.
		This object oriented approach allows you to simultaneously use several arithmetic coders, each streaming bits to a different file and to have several adaptive models for each coder, each with a different number of symbols and frequncy table.
		Written by Fred Wheeler A low precision arithmetic coding implementation avoiding hardware division is available on the same site in ftp://ftp.cpsc.ucalgary.ca/pub/projects/arithmetic.coding/low.precision.version file low.precision.version.shar Kris Popat has worked on "Scalar Quantization with Arithmetic Coding." It describes an arithmetic coding technique which is quite general and computationally inexpensive.
	www.faqs.org /faqs/compression-faq/part1/section-12.html (348 words)

	Amazon.fr : Introduction to Arithmetic Theory of Automorphic Functions: Livres en anglais: Goro Shimura (Site not responding. Last check: 2007-10-27)
		Amazon.fr : Introduction to Arithmetic Theory of Automorphic Functions: Livres en anglais: Goro Shimura
		Editeur : découvrez comment les clients peuvent effectuer des recherches sur le contenu de ce livre.
		Introduction to Arithmetic Theory of Automorphic Functions (Broché)
	www.amazon.fr /Introduction-Arithmetic-Theory-Automorphic-Functions/dp/0691080925 (359 words)

	Introduction to Sequences
		This lesson is designed to introduce students to the idea of an arithmetic sequence.
		A sequence is a list of numbers in which each number depends on the one before it.
		Explain to students that if they wish to see a sequence that is strictly arithmetic, they may enter "0" in the multiplier box.
	wps.aw.com /wps/media/objects/52/54247/lessons/pattern1.html (933 words)

	Amazon.com: Introduction to Arithmetic Theory of Automorphic Functions: Books: Goro Shimura (Site not responding. Last check: 2007-10-27)
		Advanced Topics in the Arithmetic of Elliptic Curves (Graduate Texts in Mathematics) by Joseph H. Silverman
		Introduction to Cyclotomic Fields (Graduate Texts in Mathematics) by L. Washington
		Introduction to Arithmetic Theory of Automorphic Functions by Goro Shimura $52.50
	www.amazon.com /Introduction-Arithmetic-Theory-Automorphic-Functions/dp/0691080925 (917 words)

	Math Tools Browse (Site not responding. Last check: 2007-10-27)
		This series of slides shows photographs and drawings of plants in nature that exhibit and demonstrate the Fibonacci series.
		Flash-based introduction to geometric sequences, including finding the general term, a specific term, and the sum of a range of terms.
		Flash-based introduction to arithmetic sequences, including finding the general term, a specific term, and the sum of a range of terms.
	mathforum.org /mathtools/cell/m5,7.3.9,ALL,ALL (312 words)

	Tech Report: HPL-2004-76: Introduction to Arithmetic Coding
		Abstract: This introduction to arithmetic coding is divided in two parts.
		In the second part, we cover the practical implementation aspects, including arithmetic operations with low precision, the subdivision of coding and modeling, and the realization of adaptive encoders.
		We also analyze the arithmetic coding computational complexity, and techniques to reduce it.
	www.hpl.hp.com /techreports/2004/HPL-2004-76.html (162 words)

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